Question: Simplify to lowest terms. $\dfrac{64}{48}$
Answer: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 64 and 48? $64 = 2\cdot2\cdot2\cdot2\cdot2\cdot2$ $48 = 2\cdot2\cdot2\cdot2\cdot3$ $\mbox{GCD}(64, 48) = 2\cdot2\cdot2\cdot2 = 16$ $\dfrac{64}{48} = \dfrac{4 \cdot 16}{ 3\cdot 16}$ $\hphantom{\dfrac{64}{48}} = \dfrac{4}{3} \cdot \dfrac{16}{16}$ $\hphantom{\dfrac{64}{48}} = \dfrac{4}{3} \cdot 1$ $\hphantom{\dfrac{64}{48}} = \dfrac{4}{3}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{64}{48}= \dfrac{2\cdot32}{2\cdot24}= \dfrac{2\cdot 2\cdot16}{2\cdot 2\cdot12}= \dfrac{2\cdot 2\cdot 2\cdot8}{2\cdot 2\cdot 2\cdot6}= \dfrac{2\cdot 2\cdot 2\cdot 2\cdot4}{2\cdot 2\cdot 2\cdot 2\cdot3}= \dfrac{4}{3}$